Intuitively fuzzy multi-attribute group decision making of organizational quality specificity immune evolution ability based on evidential reasoning

Abstract

Combined with the relevant theories and frameworks, this study constructs evaluation indicator and index system of organization quality specificity immune evolution ability. On the basis, this study uses the intuitively fuzzy multi-attribute decision making method based on evidential reasoning to carry out empirical analysis of organizational quality specificity immune evolution ability, empirical analysis data derive from the research objects of relevant experts, typical and representative large-sized manufacturing enterprises. The empirical analysis results indicate that the intuitively fuzzy multi-attribute decision making method based on evidential reasoning considers subjective and objective factors, which integrates the intuitively fuzzy information and gives out the corresponding decision according to the evaluation value. It is also useful, effective, feasible and operable to take the intuitively fuzzy multi-attribute decision making method based on evidential reasoning to evaluate, select and make decision choice on the best and optimal partner and investee object in multi-attribute group decision making according to organization quality specificity immune evolution ability, and give out orders of all partners and investees. The research methods and results can further improve the organization quality specificity immune efficiency, identify organization quality problems and defects, improve organization quality performance, and maintain organization health, which also provide new decision-making method for the multi-attribute groups of organization quality specificity immune evolution ability.

Keywords

Intuitively fuzzy multi-attribute group decision making evidential reasoning organizational quality specificity immune evolution ability

1 Introduction

Under the new normality of economy, the economic development of our country need to complete the conversion from the scale speed mode to the quality and efficiency mode [9], moreover, domestic and foreign market accelerated the integration, all of which make the market competition facing enterprises more intense, thus improving the quality level of the organization is the basic requirement facing the enterprises in the intense competition and changeable market environment.

And it is a key to ensure enterprises to obtain the sustainable competition advantage. The research of quality management started in the late 1980s. At present, the research on quality management has been deepened by experts and scholars, and now it has become a management science in manufacturing, service and other fields. Gradually, it is integrated into the daily production and operation process of enterprises. Under the guidance of medical metaphor thinking, the theory of organization quality management has been innovated by organizational quality specificity immunity in the field of organization quality management. In the process of self-development, the organism need to constantly interact with its survival environment, which can make the organism adapt to the environment and the production [17], resulting in a biological evolution which emphasizes self-adaption and diversity of behavior from parents to their offspring. As a new theory of organization quality management, the same organization quality specificity immunity, on the one hand, can solve the problems of organization quality management, on the one hand, when the external environment of the organization changes, the response behavior of the organization quality specificity immunity can make adjustments at any time, which requires preserving the best antibody of parents and their offspring groups of organization quality specificity immunity to adapt to environmental changes of the organization quality, ensure the smooth operation of the organization quality system, and maintain the organization health. Therefore, the organization quality specificity immune evolution ability need to be improved constantly, which will make the organization quality withstand the environmental change test, assure the response effect of the organization specificity immune, so the organization quality specificity immune evolution ability can be measured and decided scientifically, reasonably and objectively. It is not only the urgent need for the development of enterprise quality at present, but also the only way which China’s economy can develop sustainably under the quality strategy.

At present, research on the organization quality specificity immune evolution ability can be divided into two aspects. One aspect is mainly reflecting the influence of organization quality specificity immune evolution ability on organizational quality performance: Kaynak and Hartley studied the influence of the relevant interests of the organization (upstream suppliers and downstream customers) on the quality management and organization quality performance through the structural equation model [10]. Shi et al. used projection pursuit method and the forced entry method to study how the organization quality specificity immunity improved the quality performance [22]. Li et al. studied the influence of supply chain quality management immunity on organizational quality performance [40]. Pan et al. analyzed two types of immune responses including the innate immune response and the adaptive immune response in the organization quality immune system, summarized the path of improvement in the organization quality immune response ability, and emphasized the importance of the organization quality immune response on the improvement of organizational quality performance [55]. Xu et al. took technology-based SMEs as the research objects, and pointed out that the organization’s specific immune mechanisms, non-specific immune mechanisms and their integration effect can effectively help the technology-based SMEs to solve problems of environmental risks to improve organization performance [12]. On the other hand, it is to study the influence of the specific behaviors in the organization quality specificity immune evolution ability on the organizational quality performance. The organization quality specificity immune evolution ability mainly includes the improvement of three behavior abilities, such as organization quality monitoring, organization quality defense and organization quality memory. Kaynak emphasized that there was a positive relationship between the organization quality management activities and organization performance, and various quality management practices also influenced each other [11]. Flynn et al. put forward that quality management practice could be divided into two parts: basic practice of quality management and core practice of quality management [3], the organization quality defense should build a solution set to eliminate alien factors of organizational quality mainly from these two aspects. At the same time, Flynn et al. [3], Rahman and Bullock thought that the basic practice of quality management was mainly through sustained leadership support, paying attention to the customer’s expectation and encouraging employees to participate in quality management [46], while the core practice of quality management relies on the organizational process management, process product design, statistical control and other activities. From a new perspective, Choo et al. divided quality management practices into technical aspects and social aspects [2], and it was found that the technical aspects were essentially the core quality management practices, and the social aspects were just the basic quality management practices through comparative analysis. In addition, Rahman et al. [46] and Sousa et al. [44] explored total quality management and found that the purposes and ideologies of total quality management and core practice and basic practice of quality management practice were basically the same. In the post-industrial era, Li et al. used structural equation to explore the effect of quality management practices on firm performance and pointed out the effect of specific quality management practices such as customer attention, management leadership and supplier integration on firm performance [4]. Jiang et al. reviewed and summarized the interaction between different types of quality management practices and organizational quality performance, and highlighted the role of core quality management practices [29]. In addition, PP and Enter method [23], PP method, FIT method, hierarchical regression analysis [24], RAGA projection pursuit model, fitness landscape and NK model [25], meta-analysis [1] and other methods are also widely applied to the research of organization quality specificity immune evolution ability.

Through the above analysis, research on the organization quality specificity immune evolution ability is mainly focused on the influence on organizational quality performance, and the attribute of evaluation and decision contained in the organization quality specificity immune evolution ability is ignored. And the research is also short of the index selection and quantification of the organization quality specificity immune evolution ability and the results corresponding decision made according to the empirical analysis. Therefore, in order to make up for this deficiency, this paper chooses the method of intuitively fuzzy multi-attribute group decision making based on the evidential reasoning, considering both objective and subjective factors, evaluating and making decision on the organization quality specificity immune evolution ability in an objective and scientific attitude, and providing a reference for the optimal choice of partners for the enterprises, banks and other investment institutions.

2 Construction of evaluation index system of organization quality specificity immune evolution ability

The organization quality specificity immunity is a performance of an organization immunity in the quality level [22]. The organization immunity is put forward by Lv et al. who used medical metaphor thinking to work out a theory of organization immunity [31 –34], and the organization immunity is defined as: the ability for enterprises to identify external and internal dissent, and eliminate the threat factors to generate memory, so as to maintain the health of enterprises [31]. In medicine, the organization of immune behavior is divided into non-specific immunity and specific immunity. The organization specificity immunity refers to the immunity generated by the immune response in the course of organization operation and development, and it is acquired the day after the day [31]. The organization quality specificity immunity is a direct performance of an organization immunity in the quality level [3]. The organization quality specificity immunity refers to a series of acquired behaviors about the organization’s surveillance, recognition and clearance of dissident factors, and the generating of memory. The purpose is to ensure the smooth operation of the organization quality system and the organizational health. Similarly, organization quality specificity immunity mainly includes three behavior [34]: organization quality monitoring, organization quality defense and organization quality memory. Organization monitoring behavior is the starting point of organization strategic planning and the key means of the management to environmental perception, which is conducive to the organization to grasp the information of environmental changes and choose the strategy adapt to the environment [43]. The organization quality monitoring behavior is the activity of the organization to recognize and master the situation and information of uncertain factors in its environment, and the environment includes not only the external environment of the organization, such as market environment, technical environment and political and legal environment, but also the internal environment, such as staff, technical and management aspects of the organization. The organization quality monitoring behavior is the precondition of forming defense strategy and determining the optimal strategy of quality defense. The organization quality monitoring identifies the harmful factors hiding in the internal and external environment of the organization, avoids the confusion of harmful factors and beneficial factors in the process, and transmits the identified information to the internal organization, which is conducive to the organization to understand the quality of the situation, and find quality problems and defects as soon as possible to take quality prevention and quality management practice efficiently, so as to ensure the organization quality health. The higher the frequency of the organization quality monitoring, the more valuable information collected and refined, and the organization’s insight on quality information is higher, so the characteristics of organization quality monitoring scope, organization quality monitoring frequency and organization quality monitoring mode are important indicators reflecting the organization monitoring behavior [16, 42]. The organization quality defense behavior refers to a series of behavior that the organization resists and eliminates the harmful factors of the quality [24]. After receiving the organization monitoring information, the organization fully mobilizes the quality experience and knowledge of the organization, gathers quality defensive strategies of all forces, and forms a plan set of organizational quality defense and management practice. Combined with the actual situation, the organization determines the best quality defense plan. Flynn et al. divided the practice of organization quality management into the core practice of quality management (including leadership support, attention to customer needs expectation, encouraging employees to participate in quality management, etc.) and the basic practice of quality management (process management, process product design, statistical control, etc.) [3]. Kaynak validated the positive effect of the quality management practice on quality performance [11]. Song and others’ research on quality management practices focused on customer concerns and process management. Similarly, quality management practices had a positive effect on quality performance [11]. Rahman et al. [46] and Sousa [44] had further studied the practice of total quality management and divided them into hard management and soft management, but their essence was basically consistent with the purpose and idea of the core practice and basic practice of quality management. Therefore, the organization quality defense behavior can plan and configure organizational quality resources mainly through the quality management core practice, provide more immune response strategies for resources recombination. The emphasis is the strategy of mechanism, process, technology and other aspects, such as product design, process management and technical ability, etc. [4], which mainly depends on the two forms of innovating the existing resources and creating new resources to improve, and the organization needs strong improvement and innovation ability. The basic practice of quality management screens new formed immune response strategy to find the optimal solution for the organization specificity immunity behavior. The emphasis is the supporting strategies of non-mechanism and social behavior, such as leadership support, employee participation and customer orientation etc. [49], which mainly foster individual’s cognition and behavior of quality target related to organization quality, and create a sense of atmosphere of quality responsibility for the organization. To sum up, the organization quality defense can be measured from the core practice and the basic practice of organizational quality defense. Walsh stressed that the organization memory could have a protective effect on organization knowledge and information, transfer the efficient organization experience and information, which can make an enhancing learning for the organization [15]. As organization memory’s reflection in the quality level, the organization quality memory stores the information, knowledge and experience about the organization quality in the container and space loading information to achieve the goal of storage, sharing and integration of quality information, knowledge and experience to improve the decision efficiency and speed of organization quality. On the one hand, the organization quality memory can learn the organization quality immune process, and constantly enrich the organization quality knowledge system; on the other hand, it can record and summarize the organization quality immune process, store and spread these data and make a reference for future practice. Organization quality is a key factor of successfully carrying out quality management and facing the environment [7], which can improve the richness, fineness and depth of the organization quality memory, ensure the smooth operation of the organization quality system and the enterprise health, and further enhance the organization quality performance. Therefore, the characteristics, such as, organization quality memory range, organization quality memory frequency and organization quality memory mode are all important indicators to reflect the organizational quality memory.

The organization quality immunity mainly includes the organization quality monitoring, organization quality defense and organization quality memory. For the biological immunity and biological immune evolution, immune evolution includes genetic reproduction, crossover variation (including gradual change, mutation and recombination), adapted election (the key link of immune evolutionary is adaptation and selection, embodying the concept of “survival of the fittest”) [17]. Integrating the connotation, characteristics, current situation, existing problems and research topics of the organization quality specificity immunity, combining the related background and proposition with immune evolution, and collecting the evaluation index, current situation, existing problems of enterprise quality management, the organization quality specificity immune evolution ability includes genetic reproduction evolution ability, crossover variation evolution ability and adapted election evolution ability (the key link of the organization quality specificity immune evolution ability is adapted selection, embodying the concept of “survival of the fittest”) and coordinating correction (to prevent deviation) evolution ability [17]. The organization quality specificity immune evolution ability is mainly reflected in the behavior evolution effect and function evolution effect of the three aspects of the organization quality monitoring, organization quality defense and organization quality memory. The organization quality defense is divided into the soft elements of organization quality defense (basic practices, including leadership commitment and support, customer orientation, employee involvement, employee empowerment, employee training, and supplier relationship management) and the hard elements of organization quality defense (core practices, including continuous improvement and innovation, process management, statistical control and feedback, model management, product design, technical ability and analysis of information and measurement), and the hard elements of organization quality defense (core practices) is the key of the organization quality defense. In summary, referring to the related literature [1–4 , 57], this paper selects six construction dimensions to construct the evaluation index of organization quality specificity immune evolution ability, reflecting the behavior evolution effect and function evolution effect of the organization quality monitoring, organization quality defense and organization quality memory. The organization quality specificity immune evolution ability of the objective organization is evaluated from subjective and objective aspects, and ultimately the decision result is given to provide theoretical support for organization production development. The evaluation index system of organization quality specificity immune evolution ability is presented in Table 1.

Table 1
Evaluation index system of organization quality specificity immune evolution ability

Evaluation goal Construction dimension Evaluation indicator

Organization quality specificity immune evolution ability Genetic reproduction evolution Tamping and adjusting feedback of organization quality monitoring frequency

Optimization and precision of organization quality monitoring frequency (schemes, techniques, means, tools, experience, skills, techniques, methods and approaches)

Birth and maturation of organization quality monitoring strength(intensity)

Activation of organization quality monitoring width (range)

Refining and truing of organization quality monitoring depth

Expansion and extension of organization quality monitoring fertile degree (richness)

Deepening and promoting of organization quality monitoring fineness (refining)

Ratio compliance of organization quality monitoring institutions and measures

Crossover variation (soft elements of organization quality defense, basic practices) evolution Absorption - gradual change, mutation of soft elements of organization quality defense

Integration - reorganization of soft elements of organization quality defense

Promotion - reorganization of soft elements of organization quality defense

Adapted election (hard elements of organization quality defense, core practices) evolution-key link of the organization quality specificity immune evolution Absorption and adapted election of hard elements of organization quality defense Absorption and adapted election of hard elements of organization quality defense

Integration and adapted election of hard elements of organization quality defense Integration and adapted election of hard elements of organization quality defense

Promotion and adapted election of hard elements of organization quality defense Promotion and adapted election of hard elements of organization quality defense

Coordinating correction (prevent bottlenecks) evolution Tamping and adjusting feedback of organization quality memory frequency

Optimization and precision of organization quality memory frequency (schemes, techniques, means, tools, experience, skills, techniques, methods and approaches)

Birth and maturation of organization quality memory strength (intensity)

Activation of organization quality memory width (range)

Refining and truing of organization quality memory depth

Expansion and extension of organization quality memory fertile degree (richness)

Deepening and promoting of organization quality memory fineness (refining)

Ratio compliance of organization quality memory institutions and measures

3 Intuitively fuzzy multi-attribute group decision making method based on evidential reasoning

3.1 Preparatory knowledge

After Zadeh proposed the fuzzy set theory [18], and since policymakers are affected by the factors of objective environment and decision makers’ own level in evaluating information, moreover, intuitively fuzzy set can better reflect the decision makers in the evaluation process, the intuitively fuzzy set has been widely applied in multi-attribute decision problems. But for the problem of fuzzy information aggregation, different results have different emphases. In the aggregation method of some literature [8], if a membership degree of an evaluation value is zero, the membership degree of an aggregated evaluation value cannot reach the effect of final decision, at last, the decision result is not reasonable. The information aggregation method of literature [45] requires that the attribute weights of each expert must be consistent, which is meaningless to the decision of complex problems. The information aggregation of literature [56] ignores the subjective factors of weight. Therefore, this paper uses evidence reasoning to gather the intuitively fuzzy information. Evidence reasoning is a recursive algorithm based on decision theory and evidence theory. It is an effective way to integrate random information and fuzzy information. It has obvious advantage in solving the multi-attribute group decision making problem in the fuzzy environment [50]. The basic idea is to indirectly evaluate its superior indicators through direct evaluation of subordinate indicators. During this period, the proper form transformation is needed and the final evaluation result will be got through utility theory [5 , 56].

3.2 Problem description, model principle and model construction

The description of the problem, the principle of the model, and the construction of the model are detailed in the literature [5 , 56]:

Suppose that there are m programs, which are written as $P = {p_{1}, p_{2}, \dots, p_{m}}$ . Select n attribute indicators, which are written as $Q = {q_{1}, q_{2}, \dots, q_{n}}$ . Select t experts, which are written as $S = {s_{1}, s_{2}^{+}, \dots, s_{t}}$ . H = {H₁, H₂} is taken as the evaluation level set, in which $H_{1}$ represents the best level, and H₂ represents not at the excellent level. The subjective weight of the attribute index is β_j ( $β_{j} ⩾ 0, \sum_{j = 1}^{n} β_{j} = 1$ ), the expert’s subjective weight is γ_k ( $γ_{k} ⩾ 0, \sum_{j = 1}^{t} γ_{k} = 1$ ), and the expert’s comprehensive weight is λ_k ( $λ_{k} ⩾ 0, \sum_{j = 1}^{t} λ_{k} = 1$ ). The expert s_k thinks the comprehensive weight of the attribute index is $W_{j}^{k} = {w_{1}^{k}, w_{2}^{k}, \dots, w_{n}^{k}}$ ( $W_{j}^{k} ⩾ 0 \sum_{k = 1}^{t} W_{j}^{k} = 1$ ). The expert s_k records evaluation value of the attribute index q_j of the plan p_i as ( $μ_{ij}^{k}, ν_{ij}^{k}$ ). The expert s_k records the support degree of the attribute index q_j of the plan p_i at level H₁ and level H₂ as $β_{1 . j}^{k} (p_{i})$ and $β_{2 . j}^{k} (p_{i})$ , $(β_{1 . j}^{k} (p_{i}), β_{2 . j}^{k} (p_{i})) = (μ_{ij}^{k}, ν_{ij}^{k})$ . Therefore, the expert’s decision matrix is obtained, which is given by Equation (1).

$\begin{matrix} D_{k} = \\ [\begin{matrix} (β_{1.1}^{k} (p_{1}), β_{2.1}^{k} (p_{1})) (β_{1.2}^{k} (p_{1}), β_{2.2}^{k} (p_{1})) \dots (β_{1 . n}^{k} (p_{1}), β_{2 . n}^{k} (p_{1})) \\ (β_{1.1}^{k} (p_{2}), β_{2.1}^{k} (p_{2})) (β_{1.2}^{k} (p_{2}), β_{2.2}^{k} (p_{2})) \dots (β_{1 . n}^{k} (p_{2}), β_{2 . n}^{k} (p_{2})) \\ \dots \dots \dots \\ (β_{1.1}^{k} (p_{m}), β_{2.1}^{k} (p_{m})) (β_{1.2}^{k} (p_{m}), β_{2.2}^{k} (p_{m})) \dots (β_{1 . n}^{k} (p_{m}), β_{2 . n}^{k} (p_{m})) \end{matrix}] \end{matrix}$ (1)

3.3 Decision-making process

The decision-making process is detailed in documents [5 , 60]:

(1) Calculating the comprehensive weight of the target attribute index $W_{j}^{k}$ and the expert’s comprehensive weight λ_k. $W_{j}^{k}$ and λ_k are illustrated in Equations (2) and (3) respectively. $W_{j}^{k} = \frac{1 - β_{j} (E (c_{j}^{k}))}{n - \sum_{i = 1}^{n} β_{j} (E (c_{j}^{k}))} j = 1, 2, \dots, n$ (2) $λ_{k} = \frac{ρ_{k} γ_{k}}{\sum_{k - 1}^{t} ρ_{k} γ_{k}}$ (3)

Among them, where $E (c_{j}^{k})$ is the intuitively fuzzy entropy of attribute index q_j in the decision matrix D_k. $E (c_{j}^{k})$ ^,ρ_j^,M_k are illustrated in Equation (4), Equation (5) and Equation (6) respectively. $E (c_{j}^{k}) = \frac{1}{m} \sum_{i = 1}^{n} (1 - μ_{ij}^{k} - ν_{ij}^{k}) j = 1, 2, \dots, n$ (4) $ρ_{j} = \frac{1 - M_{k}}{n - \sum_{t = 1}^{k} M_{t}}$ (5) $M_{k} = \frac{1}{n} \sum_{j = 1}^{n} E (c_{j}^{k})$ (6)

(2) Calculating each expert’s support degree of different schemes at level H₁ and level H₂.

a. Calculating the basic probability assignment function $m_{r, j}^{k} (a_{i})$ and the residual probability assignment function $m_{H, j}^{k} (a_{i})$ . $m_{r, j}^{k} (a_{i})$ is given by Equation (7). $m_{H, j}^{k} (a_{i})$ is given by Equation (8). $m_{r, j}^{k} (a_{i}) = w_{j}^{k} \times β_{r, j}^{k} (a_{i})$ (7) $m_{H, j}^{k} (a_{i}) = 1 - \sum_{r = 1}^{2} m_{r, j}^{k} (a_{i})$ (8)

In this way, the basic probability assignment matrix O_k of each expert s_k can be obtained and illustrated in Equation (9). $O_{k} = {(m_{1, j}^{k} (a_{i}), m_{2, j}^{k} (a_{i}))}_{m \times n}$ (9)

Among them, $m_{2, j}^{k} (a_{i}) ⩾ 0$ , $\sum_{r = 1}^{2} m_{r, j}^{k} (a_{i}) \in [0, 1]$ , i = 1, 2, ⋯ , m ; j = 1, 2, ⋯ , n ; k = 1, 2, ⋯ , t.

b. Calculating the combination probability assignment function $n_{r, j}^{k} (a_{i})$ and the residual organization probability assignment function $n_{H, j}^{k} (a_{i})$ of the attribute indexes q_g at level H_r of different experts on each scheme. $n_{r, j}^{k} (a_{i})$ is given by Equation (10), $n_{H, j}^{k} (a_{i})$ is illustrated in Equation (11). $\begin{matrix} n_{r, j}^{k} (a_{i}) \\ = \frac{1}{σ} [n_{r, g - 1}^{k} (a_{i}) m_{r, g}^{k} (a_{i}) + n_{r, g - 1}^{k} (a_{i}) m_{H, g}^{k} (a_{i}) \\ + n_{H, g - 1}^{k} (a_{i}) m_{r, g}^{k} (a_{i})] \end{matrix}$ (10) $n_{H, j}^{k} (a_{i}) = \frac{1}{σ} n_{H, g - 1}^{k} (a_{i}) m_{H, g}^{k} (a_{i})$ (11) $σ = 1 - \sum_{f = 1}^{2} \sum_{l = 1 f \neq r}^{2} n_{f, g - 1}^{k} (a_{i}) m_{l, g}^{k} (a_{i})$ (12)

Among them, i = 1, 2, ⋯ , m ; g = 2, 3, ⋯ , n ; r = 1, 2.

c. Calculating the support degree $β_{r, j}^{k} (a_{i})$ at level H_r and the support degree $β_{H, j}^{k} (a_{i})$ at the undivided level of different experts on each scheme. $β_{H, j}^{k} (a_{i})$ is given by Equation (13). $β_{r, j}^{k} (a_{i})$ is illustrated in Equation (14). $β_{H, j}^{k} (a_{i}) = \sum_{j = 1}^{n} w_{j}^{k} (1 - \sum_{r = 1}^{2} β_{r, j}^{k} (a_{i}))$ (13) $β_{r, j}^{k} (a_{i}) = \frac{1 - β_{H, j}^{k} (a_{i})}{1 - n_{H, n}^{k} (a_{i})} n_{r, n}^{k} (a_{i})$ (14)

Among them, $\sum_{r = 1}^{2} β_{r}^{k} (a_{i}) + β_{H}^{k} (a_{i}) = 1$ , i = 1, 2, ⋯ , m ; j = 1, 2, ⋯ , n ; k = 1, 2, ⋯ , t ; r = 1, 2.

d. Constructing the decision matrix Z of support degree at level H₁ and level H₂ of different experts on each scheme. The decision matrix Z is given by Equation (15). $Z = {(β_{1, k} (a_{i}), β_{2, k} (a_{i}))}_{m \times t}$ (15)

Among them, $(β_{1, k} (a_{i}), β_{2, k} (a_{i})) = (β_{1}^{k} (a_{i}), β_{2}^{k} (a_{i}))$ ^.

(3) Calculating the comprehensive support degree of scheme p_i at level H₁ and level H₂.

a. According to $β_{r, k} (a_{i})$ , $m_{r, k} (a_{i})$ and $m_{H, k} (a_{i})$ are obtained, which are illustrated in Equation (16) and Equation (17) respectively. $m_{r, k} (a_{i}) = λ_{k} β_{r, k} (a_{i})$ (16) $m_{H, k} (a_{i}) = 1 - \sum_{r = 1}^{2} m_{r, k} (a_{i})$ (17)

Thus, the basic probability assignment function matrix Y at level H₁ and level H₂ of different experts on each scheme can be obtained, which is given by Equation (18). $Y = {(m_{1, k} (a_{i}), m_{2, k} (a_{i}))}_{m \times t}$ (18)

b. Calculating the combined probability assignment function $n_{r, y} (a_{i})$ and the residual organization probability assignment function $n_{H, y} (a_{i})$ at level H₁ and level H₂ of the expert s_y on each scheme. n_r,y (a_i) and $n_{H, y} (a_{i})$ are illustrated in Equations (19) and (20) respectively. η is given by Equation (21). $\begin{matrix} n_{r, y} (a_{i}) \\ = \frac{1}{η} [\begin{matrix} n_{r, y - 1} (a_{i}) m_{r, y} (a_{i}) + n_{r, y - 1} (a_{i}) m_{H, y} (a_{i}) + \\ n_{H, y - 1} (a_{i}) m_{r, y} (a_{i}) \end{matrix}] \end{matrix}$ (19) $n_{H, y} (a_{i}) = \frac{1}{η} n_{H, y - 1} (a_{i}) m_{H, y} (a_{i})$ (20) $η = 1 - \sum_{f = 1}^{2} \sum_{l = 1 f \neq r}^{2} n_{f, y - 1} (a_{i}) m_{l, y} (a_{i})$ (21)

Among them, i = 1, 2, ⋯ , m ; y = 2, 3, ⋯ , t ; r = 1, 2.

c. Calculating the support degree of different experts on each scheme at level H₁ and level H₂, and getting the comprehensive support degree $β_{r} (a_{i})$ and the support degree $β_{H} (a_{i})$ at the undivided level. $β_{H} (a_{i})$ and $β_{r} (a_{i})$ are illustrated in Equations (22) and (23) respectively. $β_{H} (a_{i}) = \sum_{k = 1}^{t} w_{k} (1 - \sum_{r = 1}^{2} β_{r, k} (a_{i}))$ (22) $β_{r} (a_{i}) = \frac{1 - β_{H} (a_{i})}{1 - n_{H, t} (a_{i})} n_{t} (a_{i})$ (23)

Among them, $\sum_{r = 1}^{2} β_{r} (a_{i}) + β_{H} (a_{i}) = 1$ , i = 1, 2, ⋯ , m ; r = 1, 2.

(4) Calculating the relative closeness between each scheme and each ideal scheme.

a. According to the Hamming distance of intuitively fuzzy numbers, the distance between each scheme and the positive ideal scheme $d (A_{+}, (β_{1} (a_{i}), β_{2} (a_{i})))$ and the distance between each scheme and the negative ideal scheme $d (A^{-}, (β_{1} (a_{i}), β_{2} (a_{i})))$ are obtained respectively. $d ((μ_{a}, ν_{a}), (μ_{b}, ν_{b})) \in [0, 1]$ is illustrated in Equation (24). $\begin{matrix} d ((μ_{a}, ν_{a}), (μ_{b}, ν_{b})) \\ = \frac{1}{2} [\begin{matrix} | μ_{a} - ν_{a} | + | μ_{b} - ν_{b} | + \\ | (1 - μ_{a} - ν_{a}) - (1 - μ_{b} - ν_{b}) | \end{matrix}] \end{matrix}$ (24)

b. Calculating the relative closeness degree between each scheme and the ideal scheme CC_i, and the greater the relative closeness degree CC_i, the better the scheme is. Where ${CC}_{i}$ is given by Equation (25).

$\begin{matrix} {CC}_{i} \\ = \frac{d (A^{-}, (β_{1} (a_{i}), β_{2} (a_{i})))}{d (A_{+}, (β_{1} (a_{i}), β_{2} (a_{i}))) + d (A^{-}, (β_{1} (a_{i}), β_{2} (a_{i})))} \end{matrix}$ (25)

4 Empirical analysis

The existing investment bank is looking for manufacturing enterprise to invest in projects. The bank wants to seek for the long-term and sustainable partnerships, as investor of the bank, who also wants to select the optimal investee and partner, has optimal choice in multi-attribute group decision making and sorts out the orders of the other investees and partners of manufacturing enterprises. There are four large-sized manufacturing enterprises as investment objects and research objects to be chosen and selected. Three typical and representative experts in quality management, production operation process management fields are invited to participate in the research. The four manufacturing enterprises are typical and representative in social responsibility, total assets, net profits, product market shares and qualified product rates, the number of employees of four manufacturing enterprises are all over than 1000, they all have high quality performance, they also put emphasis on quality management, organizing quality specificity immunity evolution ability and pass ISO certification. We carry out twenty-five questionnaires of senior-top managers, middle managers, basic and fundamental managers, key employees of staff for each manufacturing enterprise, they are all familiar with quality management, production operation process management of enterprises, they finish the questionnaires of organizational quality specificity immune evolution ability by intuitively fuzzy numbers. In summary, a total of 100 questionnaires are involved. Based on the 100 questionnaires, we carry out mean value processing, averaging processing, comprehensive operation processing, outlier processing, centralized processing, normalization processing and unified processing of the data. Three experts finally give out the consistent, unified and appropriate data opinions and decision matrices according to the processing and treatment results. The attribute indicator is $q_{j} (j = 1, 2 \dots 6)$ , q₁ is the genetic reproduction evolution, q₂ is the crossover variation (soft elements of organization quality defense, basic practices) evolution, q₃ is the absorption and adapted election of hard elements of organization quality defense, q₄ is the integration and adapted election of hard elements of organization quality defense, q₅ is the promotion and adapted election of hard elements of organization quality defense, and q₆ is the coordinating correction (prevent bottlenecks) evolution. The evaluation level is (r = 1, 2), H₁ represents that it is at the excellent level, and H₂ represents that it is not at the excellent level [58 , 61]. Three experts were invited to evaluate six indicators of four enterprises, and which are expressed in the form of intuitively fuzzy numbers. The subjective weight of the expert is λ = { 0.25, 0.30, 0.45 }, and the subjective weight of the attribute index is β = { 0.15, 0.20, 0.10, 0.25, 0.10, 0.20 }. The decision matrices D_k (k = 1, 2, 3) given by three experts are as follows:

$D_{1} = [\begin{matrix} q_{1} q_{2} \dots q_{5} q_{6} \\ p_{1} (0.3, 0.4) (0.6, 0.3) \dots (0.4, 0.5) (0.4, 0.5) \\ p_{2} (0.7, 0.3) (0.4, 0.2) \dots (0.6, 0.4) (0.5, 0.3) \\ p_{3} (0.6, 0.4) (0.7, 0.2) \dots (0.8, 0.2) (0.7, 0.2) \\ p_{4} (0.5, 0.2) (0.6, 0.3) \dots (0.4, 0.4) (0.4, 0.2) \end{matrix}]$

$D_{2} = [\begin{matrix} q_{1} q_{2} \dots q_{5} q_{6} \\ p_{1} (0.4, 0.2) (0.5, 0.4) \dots (0.3, 0.3) (0.5, 0.4) \\ p_{2} (0.5, 0.4) (0.5, 0.3) \dots (0.5, 0.2) (0.3, 0.3) \\ p_{3} (0.6, 0.4) (0.6, 0.4) \dots (0.5, 0.3) (0.8, 0.2) \\ p_{4} (0.5, 0.3) (0.4, 0.4) \dots (0.5, 0.4) (0.2, 0.6) \end{matrix}]$ $D_{3} = [\begin{matrix} q_{1} q_{2} \dots q_{5} q_{6} \\ p_{1} (0.3, 0.5) (0.6, 0.3) \dots (0.2, 0.4) (0.3, 0.6) \\ p_{2} (0.6, 0.4) (0.4, 0.5) \dots (0.4, 0.4) (0.2, 0.8) \\ p_{3} (0.4, 0.4) (0.2, 0.7) \dots (0.2, 0.6) (0.7, 0.2) \\ p_{4} (0.3, 0.5) (0.3, 0.7) \dots (0.3, 0.3) (0.3, 0.5) \end{matrix}]$

(1) According to the Equations (2 –6), the comprehensive weight of the target attribute index and the comprehensive weight of the experts are calculated. The comprehensive weight of the attribute index of the first expert is $w_{j}^{1} = {0.167, 0.165, 0.167, 0.166, 0.170, 0.164}$ , the comprehensive weight of the attribute index of the second expert is $w_{j}^{2} = {0.168, 0.168, 0.169, 0.162, 0.168, 0.166}$ , and the comprehensive weight of the attribute index of the third expert is $w_{j}^{3} = {0.167, 0.169, 0.170, 0.159, 0.166, 0.168}$ . The comprehensive weight of three experts is λ ={ 0.251, 0.291, 0.458 }.

(2) According to the Equations (7 –15), each expert’s support degree of different schemes at level H₁ and level H₂ is got. By the Equations (7 –9), the basic probability assignment matrix O_k (k = 1, 2, 3) of each expert are as follows:

$O_{1} = [\begin{matrix} q_{1} q_{2} q_{3} q_{4} q_{5} q_{6} \\ p_{1} (0.0501, 0.0668) (0.0990, 0.0495) (0.0501, 0.0501) (0.1162, 0.0332) (0.0680, 0.0850) (0.0656, 0.0820) \\ p_{2} (0.1169, 0.0501) (0.0660, 0.0330) (0.0668, 0.1002) (0.0996, 0.0664) (0.1020, 0.0510) (0.0820, 0.0492) \\ p_{3} (0.1002, 0.0668) (0.1155, 0.0330) (0.0835, 0.0668) (0.1162, 0.0498) (0.1360, 0.0340) (0.1148, 0.0328) \\ p_{4} (0.0835, 0.0334) (0.0990, 0.0495) (0.0501, 0.0334) (0.0498, 0.0498) (0.0680, 0.0680) (0.0656, 0.0328) \end{matrix}]$ $O_{2} = [\begin{matrix} q_{1} q_{2} q_{3} q_{4} q_{5} q_{6} \\ p_{1} (0.0672, 0.0336) (0.0840, 0.0672) (0.0676, 0.0676) (0.0972, 0.0324) (0.0504, 0.0504) (0.0830, 0.0664) \\ p_{2} (0.0840, 0.0672) (0.0840, 0.0504) (0.0845, 0.0338) (0.0810, 0.0486) (0.0840, 0.0336) (0.0498, 0.0498) \\ p_{3} (0.1008, 0.0672) (0.1008, 0.0672) (0.1014, 0.0676) (0.0486, 0.0486) (0.0840, 0.0504) (0.1328, 0.0332) \\ p_{4} (0.0840, 0.0504) (0.0672, 0.0672) (0.0676, 0.0507) (0.0648, 0.0810) (0.0840, 0.0672) (0.0332, 0.0996) \end{matrix}]$ $O_{3} = [\begin{matrix} q_{1} q_{2} q_{3} q_{4} q_{5} q_{6} \\ p_{1} (0.0501, 0.0835) (01014, 0.0507) (0.0850, 0.0680) (0.0795, 0.0477) (0.0332, 0.0664) (0.0504, 0.1008) \\ p_{2} (0.1002, 0.0668) (0.0676, 0.0845) (0.1020, 0.0680) (0.0318, 0.0795) (0.0664, 0.0664) (0.0336, 0.1344) \\ p_{3} (0.0668, 0.0668) (0.0338, 0.1183) (0.0680, 0.0850) (0.0954, 0.0318) (0.0332, 0.0996) (0.1176, 0.0336) \\ p_{4} (0.0501, 0.0835) (0.0507, 0.1183) (0.0510, 0.1190) (0.0636, 0.0318) (0.0498, 0.0498) (0.0504, 0.0840) \end{matrix}]$

According to the Equations (10 –15), the comprehensive decision matrix Z of support degree at level H₁ and level H₂ of different experts on each scheme is as follows:

$Z = [\begin{matrix} s_{1} s_{2} s_{3} \\ p_{1} (0.458, 0.359) (0.527, 0.355) (0.399, 0.419) \\ p_{2} (0.553, 0.332) (0.479, 0.266) (0.399, 0.527) \\ p_{3} (0.703, 0.246) (0.592, 0.309) (0.385, 0.313) \\ p_{4} (0.428, 0.256) (0.399, 0.372) (0.299, 0.504) \end{matrix}]$

(3) According to the Equations (16 –23), calculate the comprehensive support degree of scheme p_i at level H₁ and level H₂. According to the Equations (16 –18), the basic probability assignment function matrix Y at level H₁ and level H₂ of different experts on each scheme can be obtained.

$Y = [\begin{matrix} s_{1} s_{2} s_{3} \\ p_{1} (0.115, 0.090) (0.153, 0.103) (0.183, 0.192) \\ p_{2} (0.139, 0.083) (0.139, 0.077) (0.183, 0.241) \\ p_{3} (0.176, 0.062) (0.172, 0.090) (0.176, 0.143) \\ p_{4} (0.107, 0.064) (0.116, 0.108) (0.137, 0.231) \end{matrix}]$

According to the Equations (19 –23), the comprehensive support of each enterprise is obtained. The comprehensive support degree of the first enterprise is $(β_{1} (p_{1}), β_{2} (p_{1})) = (0.456, 0.382)$ ; the comprehensive support degree of the second enterprise is $(β_{1} (p_{2}), β_{2} (p_{2})) = (0.461, 0.403)$ ; the comprehensive support degree of the third enterprise is $(β_{1} (p_{3}), β_{2} (p_{3})) = (0.542, 0.278)$ ; and the comprehensive support level of the fourth enterprise is $(β_{1} (p_{4}), β_{2} (p_{4})) = (0.353, 0.411)$ .

(4) According to the Equations (24–25), the relative closeness degree between each enterprise and the ideal scheme is calculated. By Equation (24), the distance between each enterprise and the positive ideal scheme, and the distance between each enterprise and the negative ideal scheme are obtained. The distance between the first enterprise and the positive ideal scheme, and the distance between the first enterprise and the negative ideal scheme are as follows: $d (A^{+}, (β_{1} (p_{1}), β_{2} (p_{1}))) = 0.544$ $d (A^{-}, (β_{1} (p_{1}), β_{2} (p_{1}))) = 0.618$

The distance between the second enterprise and the positive ideal scheme, and the distance between the second enterprise and the negative ideal scheme are as follows: $d (A^{+}, (β_{1} (p_{2}), β_{2} (p_{2}))) = 0.539$ $d (A^{-}, (β_{1} (p_{2}), β_{2} (p_{2}))) = 0.597$

The distance between the third enterprise and the positive ideal scheme, and the distance between the third enterprise and the negative ideal scheme are as follows: $d (A^{+}, (β_{1} (p_{3}), β_{2} (p_{3}))) = 0.458$ $d (A^{-}, (β_{1} (p_{3}), β_{2} (p_{3}))) = 0.722$

The distance between the forth enterprise and the positive ideal scheme, and the distance between the forth enterprise and the negative ideal scheme are as follows: $d (A^{+}, (β_{1} (p_{4}), β_{2} (p_{4}))) = 0.647$ $d (A^{-}, (β_{1} (p_{4}), β_{2} (p_{4}))) = 0.569$

According to Equation (25), the relative closeness degree between each enterprise and the ideal scheme is got. The closeness degree between the first enterprise and the ideal scheme is ${CC}_{1} = 0.5318$ ; the closeness degree between the second enterprises and the ideal scheme is ${CC}_{2} = 0.5255$ ; the closeness degree between the third enterprises and the ideal scheme is ${CC}_{3} = 0.6119$ ; and the closeness between the fourth enterprises and the ideal scheme is ${CC}_{4} = 0.4765$ . Based on the criteria that the greater the relative closeness degree, the better the scheme will be, $p_{3} ≻ p_{1} ≻ p_{2} ≻ p_{4}$ can be obtained, which shows that the best investment object of the investment bank is the third manufacturing enterprise.

5 Conclusion

This paper uses the intuitively fuzzy multi-attribute decision making method based on evidential reasoning to analyze the organization quality specificity immune evolution ability comprehensively. Combined with the relevant theories and frameworks, this study firstly constructs evaluation indicator system of organization quality specificity immune evolution ability. On the basis, we adopt the intuitively fuzzy multi-attribute decision making method based on evidential reasoning to carry out empirical analysis of organizational quality specificity immune evolution ability with the help of empirical analysis data and research objects of relevant experts, typical and representative large-sized manufacturing enterprises. The empirical analysis results indicate that the intuitively fuzzy multi-attribute decision making method based on evidential reasoning considers subjective and objective factors, which integrates the intuitively fuzzy information and gives out the corresponding decision according to the evaluation value. It is also useful, effective, feasible and operable to take the intuitively fuzzy multi-attribute decision making method based on evidential reasoning to evaluate, select and make decision choice on the best and optimal partner and investee object in multi-attribute group decision making according to organization quality specificity immune evolution ability, and give out orders of all partners and investees. Through the evaluating and multi-attribute group decision making of the organization quality specificity immune evolution ability, the organization quality specificity immune evolution efficiency and evolution ability can be further improved and enhanced, and the organization can clearly identify quality problems and defects, take corresponding strategies to make up for the lack in all aspects of the organization quality monitoring, organization quality defense and organization quality memory, promote quality management development and quality evolution ability to maintain organization health and organization competitiveness.

Footnotes

Acknowledgments

This research is funded by national social science fund project (17CGL020).

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Evaluation goal	Construction dimension		Evaluation indicator
Organization quality specificity immune evolution ability	Genetic reproduction evolution		Tamping and adjusting feedback of organization quality monitoring frequency
		Optimization and precision of organization quality monitoring frequency (schemes, techniques, means, tools, experience, skills, techniques, methods and approaches)
		Birth and maturation of organization quality monitoring strength(intensity)
		Activation of organization quality monitoring width (range)
		Refining and truing of organization quality monitoring depth
		Expansion and extension of organization quality monitoring fertile degree (richness)
		Deepening and promoting of organization quality monitoring fineness (refining)
		Ratio compliance of organization quality monitoring institutions and measures
Crossover variation (soft elements of organization quality defense, basic practices) evolution		Absorption - gradual change, mutation of soft elements of organization quality defense
	Integration - reorganization of soft elements of organization quality defense
	Promotion - reorganization of soft elements of organization quality defense
Adapted election (hard elements of organization quality defense, core practices) evolution-key link of the organization quality specificity immune evolution	Absorption and adapted election of hard elements of organization quality defense	Absorption and adapted election of hard elements of organization quality defense
	Integration and adapted election of hard elements of organization quality defense	Integration and adapted election of hard elements of organization quality defense
	Promotion and adapted election of hard elements of organization quality defense	Promotion and adapted election of hard elements of organization quality defense
Coordinating correction (prevent bottlenecks) evolution		Tamping and adjusting feedback of organization quality memory frequency
		Optimization and precision of organization quality memory frequency (schemes, techniques, means, tools, experience, skills, techniques, methods and approaches)
		Birth and maturation of organization quality memory strength (intensity)
		Activation of organization quality memory width (range)
		Refining and truing of organization quality memory depth
		Expansion and extension of organization quality memory fertile degree (richness)
		Deepening and promoting of organization quality memory fineness (refining)
		Ratio compliance of organization quality memory institutions and measures